As already described, deductive knowledge comes into being owing to the inference called deduction (equation (2)), wherein knowledge claim and knowledge provenance need not be identical. Instead, knowledge provenance herein refers to pieces of definitional knowledge. There exist two categories of deductive knowledge—primary relation of ideas and secondary relation of ideas. For example, consider the concept map depicted in Figures 2 that underlies the scenario described in Figure 1(a ). The concept map boils down to following statements—(1) The manufacturing process called turning entails cutting power (Pc ), material-removal rate (MRR ), and specific cutting energy (Kc ); (2) Cutting power (Pc ) can be expressed as \(P_{c}=F_{c}v_{c}\); (3) Material-removal rate (MRR ) is given by\(\text{MRR}=a_{p}\text{fv}_{c}\); (4) Specific cutting energy (Kc ) is given by\(K_{c}=\frac{P_{c}}{\text{MRR}}\); and (5)\(P_{c}=F_{c}v_{c}\),\(\text{MRR}=a_{p}\text{fv}_{c}\), and\(K_{c}=\frac{P_{c}}{\text{MRR}}\) yield\(K_{c}=\frac{F_{c}}{\left(a_{p}f\right)}\). The first statement does not qualify as a piece of deductive knowledge; it is rather a piece of informal-induction-based knowledge, as described in the next subsection. Statements (2), (3), and (4) are examples of primary relation of ideas, whereas the last statement exemplifies secondary relation of ideas, because it has been derived from statements (2), (3), and (4) using deduction.
Statement (2) entails three pieces of definitional knowledge—cutting power, cutting force, and cutting speed—thereby collectively referring to knowledge provenance. That is, “when force is multiplied by speed, it yields power.” This provenance as well as the definitional knowledge pertaining to the cutting force and cutting speed are not explicitly described in the concept map (Figure 2). Figure 1(b ), on the other hand, explicitly describes the definitional knowledge. Therefore, knowledge can be made more meaningful from a user’s point of view by integrating the concept maps depicted in Figures 1(b ) and 2 with abovementioned provenance. Statement 3 entails four pieces of definitional knowledge—material-removal rate, depth of cut, feed rate, and cutting speed—which collectively refer to the provenance that “material removal rate refers to the volume of material removed in unit time.” Once again, this provenance and associated definitional knowledge (depth of cut, feed rate, and cutting speed) are not explicitly described in the concept map (Figure 2). Figure 1(b ), on the other hand, depicts a portion of the relevant definitional knowledge (cutting speed). Thus, by adding definitions of the depth of cut and feed rate to the concept map depicted in Figure 1(b ) and subsequently integrating it with the concept map depicted in Figure 2 and abovementioned provenance would make knowledge representation more meaningful. A similar argument is true for statement 4.